Crack the Code

Logic
Logic puzzles require you to think. You will have to be logical in your reasoning.

In an attempt to further protect his secret chicken recipe, Colonel Sanders has locked it away in a safe with a 10-digit password. Unable to resist his crispy fried chicken, you'd like to crack the code. Try your luck using the following information:

All digits from 0 to 9 are used exactly once.
No digit is the same as the position which it occupies in the sequence.
The sum of the 5th and 10th digits is a square number other than 9.
The sum of the 9th and 10th digits is a cube.
The 2nd digit is an even number.
Zero is in the 3rd position.
The sum of the 4th, 6th and 8th digits is a single digit number.
The sum of the 2nd and 5th digits is a triangle number.
Number 8 is 2 spaces away from the number 9 (one in between).
The number 3 is next to the 9 but not the zero.

Hint

A triangle number is one which can be written with one number on the first line, 2 on the second, 3 on the third etc. Like ten-pin bowling style! (The first of these are 1, 3, 6)